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In this work we revisit the classic problem of homogeneous nucleation of aliquid droplet in a supersaturated vapor phase. We consider this at differentextents of the driving force, which here is the extent of supersaturation, andcalculate a reaction coordinate (RC) for nucleation as the driving force isvaried. The RC is constructed as a linear combination of three orderparameters, where one accounts for the number of liquid-like atoms, and theother two for local density fluctuations. The RC is calculated from all-atombiased and unbiased molecular dynamics (MD) simulations using the spectral gapoptimization approach "SGOOP" [P. Tiwary and B. J. Berne, Proc. Natl. Acad.Sci. U. S. A. 113, 2839 (2016)]. Our key finding is that as the supersaturationdecreases, the RC ceases to simply be the number of liquid-like atoms, andinstead it becomes important to explicitly consider local density fluctuationsthat correlate with shape and density variations in the nucleus. All threeorder parameters are found to have similar barriers in their respectivepotentials of mean force, however, as the supersaturation decreases the densityfluctuations decorrelate slower and thus carry longer memory. Thus at lowersupersaturations density fluctuations are non-Markovian and can not be simplyignored from the RC by virtue of being noise. Finally, we use this optimized RCto calculate nucleation rates in the infrequent metadynamics framework, andshow it leads to more accurate estimate of the nucleation rate with four ordersof magnitude acceleration relative to unbiased MD.

Reaction coordinates and rate constants for liquid droplet nucleation: quantifying the interplay between driving force and memory